One of the key skills to master as a crypto investor is careful portfolio management. Here is an outline of all things portfolio management, from active to passive, and managing volatility to understanding correlation. This base knowledge for any crypto investor can help you can select the best approach for your personal investment style.

## What is Portfolio Management?

Portfolio management is the process of selecting and managing a group of investments to meet your financial objectives and risk tolerance. Understanding portfolio management will help you achieve better long term investment results. This applies to crypto and DeFi just like traditional finance, so the concepts are borrowed from TradFi but nevertheless just as valuable to know.

## Portfolio Management Styles

There are many portfolio management styles, but you can separate them into two main categories, active and passive. The main difference between the two is the time horizon that the portfolio manager aims to hold each investment.

### Active management

Active management involves the active buying and selling of individual assets frequently to maximise returns or minimise risks. This is most likely the type of portfolio management most people associate with hedge funds, where the portfolio often changes along with market conditions.

### Passive management

Passive portfolio management is the exact opposite. It is a set-it-and-forget-it investment style. The investor typically follows an index via the use of an index fund passively or buys and holds a single, often simpler portfolio for long periods.

Both styles are used widely within the cryptocurrency community. Some traders actively manage their portfolios daily, taking profits or cutting losses based on technical and fundamental factors, market sentiment, and so on. Many, however, adopt a more passive approach, buying and holding cryptocurrencies such as Bitcoin and Ethereum. If you have heard of the term HODL (Hold On for Dear Life), then you already know what passive portfolio management looks like.

If it sounds like active management is time-consuming, that’s because it is! Whether you adopt an active style of portfolio management depends not only on how much spare time you have but also on whether you have the technical knowledge to invest actively and keep abreast of the changes in the space.

## Risk and Return

Before we delve into the techniques one can use to optimise a portfolio; we should first understand that while we should care about the expected returns of an investment, we should also acknowledge its risk. We’ll outline different risk measures later on in this article, but the most important one you should know about is volatility.

### The risk of volatility

Volatility, or standard deviation (denoted by the greek sigma, or σ), is a statistical measure of the amount of uncertainty in an asset’s price movements. The higher the volatility, the higher the price deviates or moves around its average value (μ). In general, this means an asset with higher volatility can be considered riskier since the asset’s price is more likely to fluctuate.

**Let’s take bitcoin as an example:** Bitcoin’s daily volatility since the beginning of 2020 has been 4.5%, or 86% annualised. This means that 68% of any given daily price movement will fall within one standard deviation of its mean daily returns (μ ± 4.5%). Furthermore, 95% of all daily movements will fall within two standard deviations (μ ± 9%), and 99.7% of daily movements will fall within three standard deviations (μ ± 13.5%). The graph below shows how to view standard deviation when all price returns are grouped into ranges and plotted in a histogram.

One practical calculation you can do once you measure the standard deviation is to calculate their Sharpe ratio, which is the investment’s rate of return by its volatility, or standard deviation. This ratio was developed by Nobel laureate William Sharpe and will give you a quick and handy number to compare different instruments’ risk versus return. In general, the higher the Sharpe ratio, the better the risk-adjusted returns of the investment.

## Modern Portfolio Theory

Nobel laureate Harry Markowitz pioneered modern portfolio theory in 1952. The theory describes how investors can minimise their risk taken for a given return level by building portfolios of securities that work well when paired together.

Traditionally, it is common for investors to view each investment on its own merits. Let’s take the simple example of an investor looking to build a portfolio of two cryptocurrencies out of three that he has shortlisted.

Which combination of two tokens should he pick if he wants to maximise his returns? Token A should be in the portfolio given it has the highest expected returns, but should he pick token B or C as the other component? At first glance, it doesn’t seem to matter. After all, tokens B and C both have the same expected return and volatility.

But if we simulate two portfolios by combining Token A with either Token B or C, we get the following results:

Both portfolios have exactly the same return, as expected. Since Token B and C have the same expected returns, both portfolios’ returns are simply the weighted averages of the returns of each token (0.5*50% + 0.5*35% = 43%).

Both portfolios are equally attractive if you’re considering returns only. But the volatility paints a very different picture. Portfolio 1 has less than half the volatility of Portfolio 2 – how is that possible?

### Correlation

The answer is correlation. Let’s examine the time series of the returns for each asset individually:

Just by eyeballing the figures, you can see that both Tokens A and C performed very well in years 1 and 2, then underperformed in years 3 and 4, and then performed well again in year 5. On the other hand, Tokens A and B rarely moved in tandem with one another. When Token A has a great year, Token B has a bad year, and vice versa.

The correlations between each investment heavily impact the characteristics of the resulting portfolio. We can say that Tokens A and C are highly correlated (0.7), while Tokens A and B are highly negatively correlated (-0.85). By putting uncorrelated or negatively correlated assets together, they can make up for each other’s shortfalls, dampening the overall portfolio’s volatility. Similarly, putting correlated assets together means your portfolio behaves more like one single, volatile investment.

Correlation measures the degree to which two instruments’ prices move in relation to one another, relative to their means. Two assets that are both going up can still be negatively correlated! Correlation ranges between -1 and 1:

**The formula for correlation is:**

If you aren’t mathematically inclined, don’t worry. Calculating correlation is easy on a spreadsheet. All you need is the time series for two or more instruments. Here is how to set up a correlation spreadsheet.

## Diversification and asset allocation

This brings us to the concept of diversification. Since most assets aren’t perfectly correlated with one another, a portfolio will always be less volatile than the sum of its parts. In general, as you add more assets to a portfolio, the volatility of your portfolio, or risk, will decrease. If you have heard the saying ‘don’t put all your eggs in one basket’, diversification is the financial equivalent of that.

It is important to note that diversification becomes more beneficial with assets that are less correlated with one another. This is why portfolio managers often diversify by putting instruments from different asset classes, sectors, or even countries into their portfolios.

The cryptocurrency equivalent would be investing in many different kinds of tokens at the same time. For example, you could diversify by token type:

There are also other characteristics you can consider. For example, is it Ethereum-based or issued on top of some other blockchain? Does an exchange back it? Does it collect fees from a platform or service, or is it valued for its inherent utility? These are all important factors that improve the effectiveness of the mix of assets in your portfolio. The process of choosing the mix of asset types to reduce portfolio risk is called asset allocation.

## The efficient frontier

Now that we have explored the concepts of risk-return and diversification, let’s tie them together. Given two non-perfectly correlated, risky assets with different risk and return profiles, we can find weightings for Assets A and B to minimise the portfolio’s risk.

When more assets are added to the mix, we can further minimise portfolio risk. The return of the portfolio is lowered, while the risk is higher than in the minimum volatility portfolio, represented by combinations on the red line. No rational person would accept higher risk for lower returns! Also, notice that if the weighting of Asset A is too large, this results in a sub-optimal asset allocation.

Anything on the blue line is considered the most efficient allocation since maximum returns are being generated for any given level of risk. This is the efficient frontier for all possible combinations of two or more risky assets without a risk-free investment.

### Risk-free rate and the efficient frontier

What is the risk-free rate? The risk-free asset is a hypothetical asset that has zero risks and pays a fixed rate of interest. In practice, the most commonly considered risk-free assets are short-term government bonds such as US treasury bills or other government bonds with low default risk. Such assets do not exist in crypto, but the closest available thing could be rates paid on stablecoin deposits at centralised exchanges, such as Crypto.com.

Once we have introduced a risk-free asset, we are no longer bound by the efficient frontier. By adjusting the percentage of our portfolio that is allocated to the risk-free asset and risky portfolio, we can adjust our risk exposure and returns accordingly.

The capital allocation line, seen above, represents all possible combinations of the ‘tangency portfolio’ and the risk-free asset. The tangency portfolio is some mix of assets A and B, where a line drawn from the risk-free rate on the vertical axis meets our efficient frontier curve. The tangency portfolio also represents the 100% risky portfolio with the highest Sharpe ratio.

Points on the capital allocation line differ only by the proportion of risky and risk-free assets. Points on the line below the tangency represent portfolios with 0% to 100% allocation to the risk-free asset. In contrast, points on the line above the tangency are leveraged portfolios where the investor has borrowed at the risk-free rate (sold short the risk-free asset) to leverage their exposure to the tangency portfolio.

The capital allocation line shows that it’s more efficient to leverage the most efficient portfolio rather than allocating more capital to the risky asset to increase returns. As you can see, portfolios on the capital allocation line generate higher returns per unit of risk taken.

## Learning more about Portfolio Management

Now you should have an overview of how a portfolio works, through both portfolio theories, portfolio management styles, and the effectiveness of diversifying a portfolio with complementary stocks. In the next post we’ll cover Capital Asset Pricing Models and how investment risk can be split into two types: systematic and non-systematic.